Statement A (Assertion): ^2 A- ^2 A=1 is a trigonometric identity… - Vidyadip

MCQ

Statement A (Assertion): $\cos ^2 A-\sin ^2 A=1$ is a trigonometric identity.
Statement R (Reason) : An equation involving trigonometric ratios of an angle is called a trigonometric identity, if it is true for all values of the angles involved.

A
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
C
Assertion $(A)$ is true but reason $(R)$ is false.
✓
Assertion (A) is false but reason $(R)$ is true.

✓

Answer

Correct option: D.

Assertion (A) is false but reason $(R)$ is true.

(d) : We have, $\cos ^2 A=\sin ^2 A=1$ Put $A=45^{\circ}$ we pet,
$
\cos ^2 45^{\circ}=\sin ^2 45^{\circ}=\left(\frac{1}{\sqrt{2}}\right)^2-\left(\frac{1}{\sqrt{2}}\right)^2=0 \neq 1
$
$\therefore$ It is not trigonometric identity.
$\therefore \quad$ Aseertion is talce but Reason is true.

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